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THE GOLDEN RATIO IN AN ELECTRICAL NETWORK J. WLODARSK! Proz-Westhoven, Federal Republic of Germany At the end of June 1967, Poland called together an international physics olympiad for grammar-school students in Warsaw. Five countries partici- pated: Bulgaria, Poland., Romania, Czechoslovakia, and Hungary. During this competition, the following problem was presented, among others: An infinite network consists of the resistors r. Calculate the r e s i s t ance between points A and B. T A* C VVV 1—-j C T I v W ; r .-jD! D The solution of this problem can be presented in different ways. B « - — — — One quite brief version is possible as follows: Suppose the resistance of the infinite network on the right-hand side of points C and D is equal to r . If we go one step to the left from points C and D to C and D', the resistance of the network would be r • r r CTDf n r + r n in accordance with relation: _J_ = I r CTDT r + I. r n The next resistor r is added on the left behind the resistance r r T therefore, the resistance between A and B is [Continued on page 194. ] 188 •